Recent research has highlighted the role of functional relationships in introducing elementary school students to algebraic thinking. This functional approach is here considered to study essential components of algebraic thinking such as generalization and its representation, as well as the strategies used by students and their connection with…

Designing and implementing purposefully developed tasks have been linked to students' understanding of mathematical topics. We report on design principles and intentions that guided the development of "inquiry-oriented tasks." Through a qualitative analysis of the tasks, we identified seven themes that encapsulated these design…

The systematic design and analysis of tasks which can be implemented in first-year university courses and point to advanced inner- and extra-mathematically rich issues and their rationales is an open problem in the didactics of mathematics in higher education. Potentials of such tasks can be seen with regard to learning processes in the first year…

This study aims to examine the strategies developed by 7th grade students while shading different percentages of geometric shapes. The study was carried out with 113 7th graders studying at a state middle school in a province of Turkey. The data were gathered using the Shading Percentage Test, which consisted of seven tasks. Data analysis employed…

This article explores the features of students' reasoning and sense-making when computer programming and mathematics interact, specifically, using the exterior angle concept to make different regular polygons with Scratch as a programming tool. At the end of the 2019 spring term in a public elementary school, data were obtained from a pretest, a…

From an APOS (Action-Process-Object-Schema) theory perspective, learning mathematics involves construction of knowledge through mental mechanisms, which evolves between different mental structures or stages. The focus of this study is to explore how transition occurs from an Action to a Process conception, in the context of a task related to the…

This study is a case study within a three-year-long design research study. The purposes of this study are twofold. The first purpose includes investigating whether there is a significant difference in seventh-grade students' proportional reasoning skills before and after a teaching experiment conducted in line with the perspectives of Hypothetical…

The article focuses on study visits from the perspective of mathematical project work. Project work means a systematic organizing method of teaching that is based around a project. The research questions are the kinds of study visits students made, the meaning(s) of those visits, the mathematical content in the visits and how such study visits…

In this paper, we investigate the ways in which 15 year-old students conceive interrelated issues of randomness. We deal with these issues of randomness as a whole and not separately from each other, in contrast to the research so far. In order to analyse the students' ways we introduce a modification of Kyburg's Schema [(1974). "The logical…

The purpose of the study was to explore students' consistency in their notions encountering different methods in solving the same task of comparing values of certain infinite series. The participants were 93 male students aged 16-17. Applying cognitive conflict approach and the data were collected through a questionnaire administrated in two…

We report on a series of task-based interviews in which nine mathematicians were asked to evaluate a series of six mathematical arguments, purportedly produced either by fellow mathematicians or undergraduate students. In this paper, we attend to the role of context in mathematicians' responses, leading to four themes in expectations when…

In this paper we present statistical analyses of three textbooks used by Swedish teachers to support year one children's learning of mathematics. One, Eldorado, is authored by Swedish teachers, another, Favorit, is a Swedish adaptation of a popular Finnish series and the third, Singma, is a Swedish adaptation of a Singapore series. Data were coded…

In this note, we report on an implementation of discovery-oriented problems in courses on Real Analysis and Differential Equations. We explain a type of task design that gives students the opportunity to conjecture, refute and prove. What is new is that the complexity in our problems is limited and thus the tasks can also be used in homework…

This study explored prospective middle school mathematics teachers' developing understanding of geometric transformations through designing and implementing an instructional unit in a technology supported classroom environment. The instructional unit including seven activities was developed by considering past research on learners' pre-existing…

This study examines the construct of distance -- the degree of difficulty of interacting with something -- as part of activity involving children using touchscreen digital games to learn mathematics. Ten fifth-grade children engaged in video-recorded semi-structured task-based interviews in which they used two touchscreen digital mathematics games…